Basin modelling is important for oil and gas exploration and production. One of the goals of basin modelling, and often associated reservoir filling studies, is to calculate the migration of non-aqueous reactants (most commonly petroleum, which may represent one or more chemical species) in subsurface deposits of complex geometry. To accomplish this goal, the system under study will usually be described by a grid system, with each cell of the grid being assigned petrophysical properties that describe how they will affect fluid flow. Where a three-dimensional model of a basin or reservoir, consisting of porous or fractured media, (hereafter collectively referred to as a “petroleum system”) is being developed, a mesh of elements is imposed over the space under study. The mesh is usually (but not exclusively) made up of an orthogonal grid which may be cubic in shape. In an orthogonal grid, subsurface structures are represented by points in space in the x-y plane with a common value in the z plane. Each of these points in space is known as a node. If values are stored on the nodes, then values in between the nodes are commonly calculated by interpolation (although they may be held constant throughout the element, depending on the property). There can be millions of grid cells and associated nodes in a subsurface model. The usual technique of prior art systems has been to impose, and to populate the cells of this grid based on the element(s) that contribute most to the volume of each cell.
While this conventional approach captures many coarse features of the mesh, the grid can result in a model which is crude when compared the real world, incorporating considerable inherent elements of uncertainty. Such crudeness often distorts or destroys details that are important in determining the correct migration of reactants within the mesh. Thin features with high impedance to migration may be averaged out or omitted entirely in the conversion to the grid.
As a result, efforts have been made to provide grids which more closely approximate the features of a subsurface field under review. Several of such known methods used to simulate multi-phase petroleum flow are commonly described as Darcy flow, Flowpath and Invasion Percolation. All of these methods have been successfully applied and their strengths have been well documented, but all are also characterized by weaknesses which have limited their application and the quality of the results. For example, by imposing a regular grid and converting all internal inclined planes into horizontal planes in a staircase configuration, internal watersheds, natural directions of flow, are poorly approximated by such staircase structures, possibly resulting in migration pathways that are inconsistent with the underlying geometry.